M. Coons

most citedTranscendence of the Gaussian Liouville number and relatives

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math.NT2008

(Non)Automaticity of number theoretic functions

Michael Coons

Denote by $λ (n)$ Liouville's function concerning the parity of the number of prime divisors of $n$ . Using a theorem of Allouche, Mendès France, and Peyrière and many classical resu…

math.NT2008

Completely multiplicative functions taking values in ${- 1, 1}$

Peter Borwein, Stephen K. K. Choi, Michael Coons

Define {\em the Liouville function for $A$ }, a subset of the primes $P$ , by $λ_{A} (n) = (- 1)^{Ω_{A} (n)}$ where $Ω_{A} (n)$ is the number of prime factors of $n$ coming from $A$ counting…

math.NT2008★ 1 cited

Transcendence of the Gaussian Liouville number and relatives

Peter Borwein, Michael Coons

{\em The Liouville number}, denoted $l$ , is defined by $l := 0.100101011101101111100...,$ where the $n$ th bit is given by ${1/2}(1+\gl(n))$; here $\gl$ is the Liouville function fo…

math.NT2008

Transcendence of Power Series for Some Number Theoretic Functions

Michael Coons, Peter Borwein

We give a new proof of Fatou's theorem: {\em if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function.} This res…

(Non)Automaticity of number theoretic functions

Completely multiplicative functions taking values in {−1,1}

Transcendence of the Gaussian Liouville number and relatives

Transcendence of Power Series for Some Number Theoretic Functions

Completely multiplicative functions taking values in ${- 1, 1}$